To find the measure of angle 6, we can use the fact that angles 3 and 6 are vertical angles (opposite angles formed by the intersection of two lines). Therefore, their measures are equal.
Given that[tex]\( m\angle 3 = 105^\circ \), we have \( m\angle 6 = m\angle 3 = 105^\circ \).So, the measure of angle 6 is \( \boxed{105^\circ} \).[/tex]
The measure of angle 6 is 105 degrees. This is because angles 3 and 6 are vertical angles, meaning they are formed by intersecting lines and are opposite each other. According to the Vertical Angles Theorem, vertical angles are congruent, meaning they have the same measure. Therefore, if angle 3 measures 105 degrees, angle 6, being its vertical angle, also measures 105 degrees. This principle holds true regardless of the specific configuration of lines or shapes, as long as the angles are formed by intersecting lines. Hence, in this case, the measure of angle 6 directly corresponds to the measure of angle 3 due to their relationship as vertical angles, resulting in both having a measure of 105 degrees.
If an equation is an identity, then how many solutions does it have?
Infinite is the answer
A school has two pathways through the math program. At this school,
two-sevenths of students follow the first path, and the rest take the second path. During one semester, 35% of the students who follow the first path pass the program, while 70% of the students who follow the second path pass it. Find the fraction of students who take the first path and pass.
what is 5/6 divided by 1/12
The s/n ration for a set of 50 measurements is 10. what number of measurements would make the s/n ratio 5
Find the slope at tangent line f(x)=(3/2)x+1 at (-2,-2)
What percent of the first 10 natural numbers are prime numbers?
[tex]\boxed{{\mathbf{40\% }}}[/tex] of the first 10 natural numbers are prime numbers.
Further explanation:
The prime numbers are the numbers that is only divisible by 1 and itself and greater than 1.
Natural numbers are the numbers that is easily countable as their successors can be defined and its starts from 1.
The natural number can be expressed as,
[tex]1,2,3,4,5,6,7,8,9,10 \ldots[/tex]
Step by step explanation:
Step 1:
First determine the first ten natural numbers.
[tex]1,2,3,4,5,6,7,8,9,10[/tex]
Step 2:
Now determine the prime numbers among the first ten natural numbers.
The prime numbers among the first ten natural number are [tex]2,3,5,7[/tex].
Therefore, there are 4 prime numbers.
Step 3:
Now, find the percentage of the first 10 natural numbers are prime numbers.
In general the percentage of any number can be calculated as,
[tex]{\text{percent of }}x = \dfrac{x}{{{\text{total number}}}} \times 100[/tex]
The percentage of the prime numbers can be calculated as,
[tex]\begin{aligned}{\text{percent of prime number}}& = \frac{4}{{{\text{10}}}} \times 100\\ &= 40\% \\\end{aligned}[/tex]
Therefore, [tex]40\%[/tex] of the first 10 natural numbers are prime numbers.
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Percentage
Keywords: Integers, expression, natural numbers, prime numbers, percentage, denominator, numerator, fractions, divisible, total number, the required number
your local gas stations are having a price war during the past seven days they have lowered the price of regular gas by $0.2 each day define a variable then write and solve an equation to find the total change in gas price show your work
Let x denotes the number of days and y denotes the total change in gas price ( in dollars).
Given : During the past seven days the price of regular gas is decreased by $0.2 each day.
Rate of decrease =$0.2 per day
Then , Total change in gas price = Rate of decrease x Number of days
i.e.[tex]y= 0.2 \times x[/tex]
i.e. [tex]y=0.2x[/tex] (1)
To find the total change in gas price in 7 days , we put x= 7 in (1) , we get
[tex]y=0.2(7)=1.4[/tex]
Hence, the total change in gas price in 7 days = $1.4
Answer:
0.14
Step-by-step explanation:
Let t be the total reduction. Then ...
t = daily change * number of days
t = 7 * 0.02
t = $0.14!
What is 25 divided by 28
The solution after divide is,
⇒ 0.893
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
To divide the numbers,
⇒ 25 divided by 28
Now, We can divide the numbers as;
⇒ 25 divided by 28
⇒ 25 ÷ 28
⇒ 25 / 28
⇒ 0.893
Thus, The solution after divide of the numbers is,
⇒ 0.893
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Stacy made a deposit of $8,500.00 into an account. After ten years, the account had earned $5,525.00 in interest. What simple interest rate did the account earn?
xm-2m if x=-2 and m=-3
xm-2m
x=-2, m = -3
xm = -2 *-3 = 6
2m = 2*-3 = -6
6- -6 = 6+6 = 12
Nia has number cards for 2,3,8,9 and 5. What are all the different ways Nia can arrange the cards to show only even numbers with the 2 in the ten- thousands place?
A drinking glass has height of 4 inches in height,in a length of 2 inches and 2 inches in width,while a baking pan has a width of 4 inches lenght of 8 inches and a depth of 2 inches.if the baking pan is filled of water up to its half depth using the drinking glass,how many glasses of full water would be needed?
There are 2 glasses of full water would be needed to fill the baking pan.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A drinking glass has height of 4 inches ,in a length of 2 inches and 2 inches in width.
And, A baking pan has a width of 4 inches length of 8 inches and a depth of 2 inches.
Now,
The volume of drinking water = 4 x 2 x 2
= 16 inches³
And, The volume of baking pan = 4 x 8 x 2
= 64 inches³
So, Half depth of baking pan = 64 / 2
= 32 inches³
Here, The volume of drinking water = 16 inches³
Thus, Number of glass of full water would be needed to fill the baking pan = 32 / 16 = 2
Therefore, There are 2 glasses of full water would be needed to fill the baking pan.
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Write 15 is no more than a number T divided by 5 as an inequality ( great than less than...)
The inequality representing '15 is no more than a number T divided by 5' is written as 15 <= T/5, which means T divided by 5 should be greater than or equal to 15.
The phrase '15 is no more than a number T divided by 5' can be translated into an inequality. When we interpret 'no more than', it means 'less than or equal to'. Therefore, the statement can be translated into the inequality 15 <= T/5. This expresses that when you divide the number T by 5, the result should be at least 15 or any value less than 15. The interpretation of "no more than" as "less than or equal to" clarifies the inequality's meaning, emphasizing that the resulting quotient from dividing T by 5 should not exceed 15. Thus, the inequality encapsulates the relationship between the number 15 and T when considering their division by 5.
The minimum sustained wind speed of a category 1 hurricane is 74 miles per hour. The maximum sustained wind speed is 95 miles per hour. Write an absolute value equation that represents the minimum and maximum speeds. Let V represent the wind speed.
The absolute value equation that represents the range of a category 1 hurricane's wind speed is |V - 84.5| ≤ 10.5. 84.5 is the average of the range and 10.5 is the difference from the range's center to the end.
Explanation:The absolute value equation that represents the minimum and maximum sustained wind speeds of a category 1 hurricane can be written as |V - 84.5| ≤ 10.5. Here, V stands for the wind speed. The middle value of 74 and 95 is 84.5 (the average of 74 and 95). And the distance from 84.5 to either end of the range (74 or 95) is 10.5. So, the range of speeds is represented by the absolute difference from the center of the range is less than or equal to 10.5.
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It takes 23 minutes for 6 people to paint 6 walls. How many minutes does it take 9 people to paint 9 walls?
Answer:
23
Step-by-step explanation:
Imagine that each person is assigned one wall, and all 6 people begin painting at the same time.
Since everyone will finish painting their assigned wall after 23 minutes, it takes one person 23 minutes to paint one wall.
If we have 9 people and 9 walls, we can again assign one wall to each person.
Everyone will take 23 minutes to paint their assigned wall.
In other words, it takes 23 minutes for 9 people to paint 9 walls.
The Des Plaines River Bridge is 2.1 km long. Engineers are considering re-lighting the bridge with a pole placed every 100 feet of the bridge length starting from the south end. Each pole will support four light globes. How many globes will be required for the re-lighting project?
Fifteen people volunteer for a park cleanup. The number of volunteers increases by 7 people each month for several months. After how many months will there be 50 volunteers
Tony says that 4,400 is halfway between 4,000 and 5,000.is he correct?why or why not?
Tony is not correct. The midway point between 4,000 and 5,000 is found by calculating the average of the two numbers, which is 4,500. Therefore, the halfway point is 4,500, not 4,400.
Explanation:Tony states that 4,400 is halfway between 4,000 and 5,000. To determine if Tony is correct, we need to find the midpoint between the two numbers. The midpoint can be found by adding the two numbers together and dividing by 2:
(4,000 + 5,000) / 2 = 9,000 / 2 = 4,500.
Therefore, the exact halfway point between 4,000 and 5,000 is 4,500. This means that Tony's assertion that 4,400 is halfway between these two numbers is not correct; the correct halfway point is actually 4,500.
No, Tony is not correct. Halfway between 4,000 and 5,000 would be the average of the two numbers, which is 4,500.
Explanation:No, Tony is not correct. Halfway between 4,000 and 5,000 would be the average of the two numbers. To find the average, we add the two numbers together and divide by 2. In this case, the average of 4,000 and 5,000 would be (4,000 + 5,000) / 2 = 9,000 / 2 = 4,500. Therefore, 4,400 is not halfway between 4,000 and 5,000.
You can buy DVDs at a local store for $15.49 each. You can buy them at an online store for $13.99 each plus $6 for shippimg. How many DVDs can you buy for the same amount at the two stores
To find out how many DVDs you can buy for the same price at both stores, you create a formula incorporating the cost per DVD and the shipping cost at the online store. Solving this equation will give you the number of DVDs where the cost will be equal at both stores. However, this might not always result in a whole number, indicating that there is no exact count of DVDs resulting in the same cost.
Explanation:To determine how many DVDs you can buy for the same amount at both stores, you can set up a mathematical equation accounting for the cost of each DVD and the shipping cost in the online store. The equation would look like this:
15.49 x = 13.99 y + 6
where x and y represent the number of DVDs bought from the local and online store respectively. By solving this equation we're finding out for which number of DVDs the total costs at both stores are equal.
To find the exact number of DVDs where the total cost will be the same, the equation needs to be solved for a whole number. This may result in no exact integer solution, showing that there's no exact number of DVDs for which the cost will be the same at both stores.
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Explain how you can find 4 × 754 using two different methods
If the manager at first city bank surveys a sample of 100 customers to determine how many miles they live from the bank, is the mean travel distance for this sample considered a parameter or a statistic? explain.
The mean travel distance for the sample of 100 customers surveyed by the manager at First City Bank is considered a statistic.
Explanation:The mean travel distance for the sample of 100 customers surveyed by the manager at First City Bank is considered a statistic.
In statistics, a parameter is a numerical characteristic of the whole population that can be estimated by a statistic. Since the manager is surveying only a sample of customers, the mean travel distance calculated from this sample is a statistic, not a parameter.
For example, if the manager had surveyed all customers of First City Bank, then the mean travel distance calculated from that data would be a parameter.
estimate the answer to 109 divided by 96
Solve (1-sin(x))(1+sin(x))
What is the equation of the circle shown in the graph
Answer: its the third option
meg knows that it takes 16 minutes for her to read 7/x of a chapter. How long will it take her to read the entire chapter?
How do you write 15 cubed in exponential notation
Each side of a square is increasing at a rate of 3 cm/s. at what rate is the area of the square increasing when the area of the square is 16 cm2?
Answer:
The rate of the area increasing for square is 24cm²/ s
Rate of increasing side ?
Changing the length of side with respect to time is the rate of increasing side .
Given each side of square is increasing at a rate 3cm/s.
Area of square = sides²
Side length = a
(dA/dt) = (dA/da)×(da/dt) { chain rule of differentiation}
Differentiation of area w.r.t. t is
dA/da= 2a (da/dt)
dA/dt = 2a *(da/dt)
da/dt = 3 cm/s
When A=16 cm²
16 = a²
a= 4
(dA/dt) = 2x4 x 3
= 24 cm²/ s
Hence, the rate of the area increasing for square is 24cm²/s
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What is the contrapositive of the conditional statement? If two variables are directly proportional, then their graph is a linear function.
What's 307, 407 rounded to the nearest thousand?
what all fractions are equivalent to 1.27 repeating